Problem: Simplify; express your answer in exponential form. Assume $t\neq 0, q\neq 0$. $\dfrac{{t^{-3}}}{{(t^{5}q^{-5})^{-4}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${t^{-3}}$ to the exponent ${1}$ . Now ${-3 \times 1 = -3}$ , so ${t^{-3} = t^{-3}}$ In the denominator, we can use the distributive property of exponents. ${(t^{5}q^{-5})^{-4} = (t^{5})^{-4}(q^{-5})^{-4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{t^{-3}}}{{(t^{5}q^{-5})^{-4}}} = \dfrac{{t^{-3}}}{{t^{-20}q^{20}}}$ Break up the equation by variable and simplify. $\dfrac{{t^{-3}}}{{t^{-20}q^{20}}} = \dfrac{{t^{-3}}}{{t^{-20}}} \cdot \dfrac{{1}}{{q^{20}}} = t^{{-3} - {(-20)}} \cdot q^{- {20}} = t^{17}q^{-20}$.